The quantities \(\mbox{Wg}(\ell (\sigma \vee \tau ))\)  appearing in (REF ) are the orthogonal Weingarten functions, and depend upon the dimension \(d=n-1\)  as well. They have been computed up to order \(q=6\)  [1]}. For \(q=4\)  :
\(\mbox{Wg}(1^4)= & \: \phi \: (n-3)(n+2)(n^2+4n-4) \\\mbox{Wg}(2,1,1)= & \: \phi \: (-n^3-3n^2+6n+4)\\\mbox{Wg}(2,2)= & \: \phi \: (n^2+3n+14) \\\mbox{Wg}(3,1)= & \: \phi \: (n-1)(2 n+6)\\\mbox{Wg}(4)=& \: - \phi \: (5n+1)\) 
\(\mbox{where}\qquad \phi = \frac{1}{(n-4)(n-3)(n-2)(n-1)n(n+1)(n+3)(n+5)}\hspace{5.0pt}.\) 
